Hahahaha, the one that comes immediately to mind isn't a manga. 10 things I hate about you.

I remember that movie, it was quite good.

The OP is not looking for any manga based on Shakespeare's play but for a particular story:

A man has two daughters, the elder has horrible personality while the younger one is the opposite of her sister (though in the movie she was horrible in her own way). The man wants to marry off his daughters in order, but only the younger one is popular with guys. Eventually some guy appears who tries to hit on the older daughter, but he does it just for the money (at least at first).

Let's see:Girl has horrible personality and thus is unpopular. Some guy starts hitting on her for some reason other than love, but eventually falls in love with her for real.